Recent questions tagged q1-1

Write the negation of "For every positive real number $x$, the number $x+1$ is also positive."

asked Aug 4, 2014 by rvidyagovindarajan_1

1 answer

Write the negation of "For every positive real number $x$, the num ber $x+1$ is also positive."

asked Aug 4, 2014 by rvidyagovindarajan_1

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Show that the statement " If $x$ is real number such that $x^3+4x=0$, then $x$ is 0." is true using direct method.

asked Jul 25, 2014 by rvidyagovindarajan_1

1 answer

Identify the connecting word and and write the components of the statement "All rational numbers are real and all real numbers are not complex."

asked Jul 16, 2014 by rvidyagovindarajan_1

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Write the negation of "Chennai is the capital of Tamil Nadu."

asked Jul 14, 2014 by rvidyagovindarajan_1

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There are $35$ days in a month. Is this sentence a statement? Give reason.

asked Jul 3, 2014 by rvidyagovindarajan_1

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Find the coordinates of the point which divides the line segment joining the points $(-2,3,5)$ and $(1,-4,6)$ in the ratio $2:3$ internally.

asked May 5, 2014 by rvidyagovindarajan_1

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Find the distance between the points $(2,3,5)$ and $(4,3,1)$

asked Apr 16, 2014 by rvidyagovindarajan_1

1 answer

Find all the value of the following : $(i)^{\large\frac{1}{3}}$

asked Jun 12, 2013 by sreemathi.v

1 answer

Evaluate the limit for the following if exists.$\;\lim\limits_{x\to 2} \large\frac{\sin \pi x}{2 - x}$

asked May 6, 2013 by poojasapani_1

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Find the intervals of concavity and the points of inflection of the following functions:$f(x)=(x-1)^{1/3}$

asked May 6, 2013 by poojasapani_1

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Find the critical numbers and stationary points of each of the following functions.$\;f(x)=2x-3x^{2}$

asked May 5, 2013 by poojasapani_1

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Prove the following inequalities: $\cos x> 1-\large\frac{x^{2}}{2}, $$x>0$

asked May 4, 2013 by poojasapani_1

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Evaluate the limit for the following if exists,$\;\lim\limits_{x \to 2} \large\frac{\sin\pi x}{2-x}$

asked May 4, 2013 by poojasapani_1

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Obtain the Maclaurin's series expansion for:$\;e^{2x}$

asked May 4, 2013 by poojasapani_1

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Verify Lagrange's law of mean for the following function;\[\]$f(x)=1-x^{2} \quad [0,3]$.

asked May 3, 2013 by poojasapani_1

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Verify Rolle's theorem for the following function; $f(x)=\sin x, 0\leq x\leq\pi$.

asked May 3, 2013 by poojasapani_1

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Find the equation of the tangent and normal to the curves. $y=x^{2}-4x-5$ at $\;x=-2$

asked May 1, 2013 by poojasapani_1

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A missile fired from ground level rises $x$ metres vertically upwards in $t$ seconds and $x=100t-\large\frac{25}{2}t^{2}$ find the initial velocity of the missile.

asked Apr 30, 2013 by poojasapani_1

1 answer

Find the area of the region bounded by the lines $x-y=1 $ and $x$-axis,$x=2$ and $x=4$

asked Apr 27, 2013 by poojasapani_1

1 answer

Evaluate: $\int\limits\sin^{4} x dx$

asked Apr 27, 2013 by poojasapani_1

1 answer

Verify $\large\frac{\partial ^{2} y}{\partial x\partial y}=\frac{\partial ^{2} y}{\partial y\partial x}$ for the following function;$\;u=x^{2}+3xy+y^{2}$

asked Apr 24, 2013 by poojasapani_1

1 answer

Find the differential of the functions.$y$$=x^{5}$

asked Apr 24, 2013 by poojasapani_1

1 answer

If $X$ a normal variate with mean $80$ and standard deviation $10$ compute the following probabilities by standardizing. $P(X\leq$100$)$

asked Apr 22, 2013 by poojasapani_1

1 answer

Let $X$ have a poisson distribution with mean $4$.Find $(i) \;P(X\leq $3$)\qquad[e^{-4} = 0.0183].$

asked Apr 21, 2013 by poojasapani_1

1 answer

Find the value of 'p' for which the following equation represents a pair of straight lines : $x^2+pxy-2y^2+3gx+3fy=0.$

asked Apr 18, 2013 by sreemathi.v

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Given that $A=\begin{bmatrix}\cos x & \sin x\\-\sin x& \cos x\end{bmatrix}$ and $A(adj. A)=K\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}$,find the value of K.

asked Apr 17, 2013 by sreemathi.v

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Solve for x and y : $\begin{bmatrix}x^2\\y^2\end{bmatrix}+2\begin{bmatrix}2x\\3y\end{bmatrix}=3\begin{bmatrix}7\\-3\end{bmatrix}$

asked Apr 16, 2013 by sreemathi.v

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If $A\begin{bmatrix}1 & 2\\2 & 1\end{bmatrix}$,show that $A^2-3I=2A$.

asked Apr 16, 2013 by sreemathi.v

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Find $x$ and $y$,if $x+y=\begin{bmatrix}7 & 0\\2 & 5\end{bmatrix}$ and $x-y=\begin{bmatrix}3 & 0\\0 & 3\end{bmatrix}$.

asked Apr 15, 2013 by sreemathi.v

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Find the order and degree of the following differential equation: $\large\frac{dy}{dx}+y$=$x^{2}$

asked Apr 14, 2013 by poojasapani_1

1 answer

Find the equation of the asymptotes to the hyperbola $36x^{2}-25y^{2}=900$

asked Apr 13, 2013 by poojasapani_1

1 answer

If $M(\theta)=\begin{bmatrix}\cos \theta & \sin\theta\\-\sin\theta &\cos\theta\end{bmatrix}$,show that $M(x)M(y)=M(x+y).$

asked Apr 12, 2013 by sreemathi.v

1 answer

If a matrix $A=\begin{bmatrix}6 & x & 2\\-2 & -1 & 2\\-10 & 5 & 2\end{bmatrix}$ is a singular matrix,find the value of x.

asked Apr 11, 2013 by sreemathi.v

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Find the equation of the tangent and normal to the parabola $y^{2}=12x $ at $ (3 , -6 )$

asked Apr 11, 2013 by poojasapani_1

1 answer

Find the equation of the hyperbola if focus : $(2 , 3 );$ corresponding directrix : $x+2y=5,e=2$

asked Apr 11, 2013 by poojasapani_1

1 answer

If A=$\begin{bmatrix}3 & -2\\4 & -2\end{bmatrix}$,find x such that $A^2=xA-2I.$Hence find $A^{-1}$.

asked Apr 11, 2013 by sreemathi.v

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Find the equation of the ellipse if One of the foci is$(0 , -1 )$, the corresponding directrix is $3x+16=0$ and $e=\large\frac{3}{5}$

asked Apr 10, 2013 by poojasapani_1

1 answer

Solve for x and y if $\left(\begin{array}{c}x^2\\y^2\end{array}\right)+2\left(\begin{array}{c}2x\\3y\end{array}\right)=3\left(\begin{array}{c}7\\-3\end{array}\right)$

asked Apr 10, 2013 by sreemathi.v

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Find the equation of parabola if : Focus:$(2 , -3 );$ directrix :$2y-3=0$

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the angle between the followin planes: $2x+y-z=9 $and $x+2y+z=7$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the shortest distance between the parallel lines $\overrightarrow{r}=(\overrightarrow{2i}-\overrightarrow{j}-\overrightarrow{k}) + t (\overrightarrow{i}-\overrightarrow{2j}+\overrightarrow{3k})$ and $\overrightarrow{r}=(\overrightarrow{i}+\overrightarrow{2j}+\overrightarrow{k}) + s (\overrightarrow{i}-\overrightarrow{2j}+\overrightarrow{3k})$

asked Apr 7, 2013 by poojasapani_1

1 answer

Is the function $f(x) = 5x-3$ continous at $x=0$?

asked Apr 4, 2013 by balaji.thirumalai

1 answer

Express the following in the standard form $a + ib$: $\large\frac{2\left ( i-3 \right )}{\left ( 1+i \right )^{2}}$

asked Apr 1, 2013 by geethradh

1 answer

Express the following in the standard form $a + ib$: $\frac{2(i-3)}{(1+i)^2}$

asked Apr 1, 2013 by balaji.thirumalai

0 answers

Examine the consistency of the following system of equation. If it is consistent than solve the same. $4x+3y+6z=25\;,x+5y+7z=13\;,2x+9y+z=1 $

asked Mar 30, 2013 by poojasapani_1

1 answer

Find the adjoint of the following matrices $\begin{bmatrix} 3 & -1 \\2 & -4& \end{bmatrix}$

asked Mar 27, 2013 by poojasapani_1

1 answer

Given Relation $R$ in the set $A=\{1,2,3,...,13,14\}$ defined as $R=\{(x,y):3x-y=0\}$. Which of the following is true?

asked Mar 7, 2013 by balaji.thirumalai

1 answer

Find the transpose of each of the following matrices :$ (i) \begin{bmatrix} 5 \\ \tfrac{1}{2} \\ -1 \end{bmatrix}$

asked Mar 1, 2013 by balaji.thirumalai

1 answer

Let $ A\;=\begin{bmatrix}2 & 4\\3 & 2\end{bmatrix}, B\;=\begin{bmatrix}1 & 3\\-2 & 5\end{bmatrix}, C\;=\begin{bmatrix}-2 & 5\\3 & 4\end{bmatrix}$. Find $\;A+B\qquad$

asked Feb 27, 2013 by balaji.thirumalai

1 answer

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